Second monitor iMac 2011

Use your iMac as a display with target display mode - Apple Support

The 2011 iMac can be used as a display for a new Mac. You will need a Thunderbolt 3 adapter

Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple

and a Thunderbolt cable.

https://www.apple.com/shop/product/MD861LL/A/apple-thunderbolt-cable-20-m

You can connect any of these older iMac models to another Mac from 2019 or earlier for use as an external display. Learn how to identify your iMac model.

• 27-inch iMac models introduced in 2009 and 2010: Use a Mini DisplayPort cable to connect your iMac to a Mini DisplayPort or Thunderbolt or Thunderbolt 2 port on the other Mac.
• All iMac models introduced in 2011, 2012, 2013, and mid 2014: Use a Thunderbolt cable to connect your iMac to a Thunderbolt or Thunderbolt 2 port on the other Mac. If the other Mac uses Thunderbolt 3, you can use the Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter with your cable.

Target display mode requires macOS High Sierra or earlier on the iMac used as the external display. It does not work with macOS Mojave or later.

This is Target Display Mode:

Target Display Mode isn’t supported on iMac models with Retina display.

It is only supported on iMac (27-inch, Late 2009), iMac (27-inch, Mid 2010), and iMac (Mid 2011 to Mid 2014) support Target Display Mode.

(reference: https://support.apple.com/guide/mac-help/use-an-imac-as-a-display-mh30822/10.14/mac/10.14)

Your old mid 2011 21.5 Supports it

But the new one your are going to buy will NOT support it.

Unless you find a good used one, at most mid 2014.

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Lets cry? It depends. For what is the purpose?

if you don't need more than 25FPS and just want to use the other as an auxiliar monitor (for anything that is not faster than 25FPS, there are some software solutions which does "airplay' to the other Mac.

Its not like having the Target Display Mode, its far from that, but for some situations its good. Software airplay works on any Mac to use another as a second monitor, but its like having a Remote Desktop view (faster than VNC), but not for video jobs.. but good for office, internet and alike.

No.

yes but you need a thunderbolt to thunderbolt 3 (usb c) adaptor

That is correct, iMacs are computers, not external displays.

The new iMac can't be used as a display, but the 2011 one can, with. the Thunderbolt adapter and cable. It will need a keyboard to enter the code to start Target Display Mode.